Due to the frequency offset between the transmitting device and the receiving device, and the Doppler shift caused by the movement of the transmitting device in the wireless communication system, the frequency between the carrier frequency received by the receiving device and the frequency of the local crystal oscillator are present, it is named frequency offset. Especially in an area of a high-speed railway, which covered by a mobile communication system, the device (user equipment) has a high moving speed (e.g. in an area of a high-speed railway, which covered by a mobile communication system, the moving speed of the devices are generally more than 300 km/h). It brings about a serious Doppler effect. The maximum Doppler frequency can be reached more than 1500 Hz, which caused the deviation of the base state's frequency adoption, and the serious constellation point's phase rotation of equalizer's outputs, it leads to incorrect demodulation and decoding of equalizer.
Current methods for eliminating the frequency offset caused by the Doppler Effect are: estimation of the frequency offset, compensation of the sampling deviation, and phase rotation, in order to eliminate the influence of the Doppler shift as much as possible. For instance, it utilizes a cyclic prefix for coarse frequency offset estimation and pre-compensation. However, the signal/noise ratio in the actual environment cannot be guaranteed, the error of the coarse frequency offset estimation is huge, or even invalid, and the frequency offset cannot be accurately compensated.